Application of Monte Carlo Integral Method in Slope Stability Analysis

This study focuses on a critical challenge: accurately calculating the weight of sliding masses with complex geometries. To address this issue, the study systematically examines the use of Monte Carlo integration in slope stability analysis. Conventional analytical methods, such as the slice method, frequently encounter limitations due to their reliance on simplistic assumptions under complex boundary conditions, resulting in suboptimal accuracy or computational inefficiency. In order to surmount these limitations, the present research employs the Monte Carlo integration method in combination with the bounding box technique in an innovative manner. The findings indicate that computational accuracy can be flexibly regulated by modifying the number of random samples. As the sample size increases, the error value decreases gradually and stabilises. When the sample count reaches the order of 10⁷, the relative error in volume calculation remains within 0.0061%. In the two- and three-dimensional slope models with irregular slope boundaries, this approach enables efficient calculation of the area and volume of sliding masses with arbitrary shapes. The present study has sought to compare and contrast the validity of Monte Carlo integration with that of traditional methods. The findings of this investigation have been such that Monte Carlo integration has been shown to maintain computational stability and efficiency, whilst also exhibiting superior adaptability to complex boundary conditions. The proposed methodology can be further extended to develop quantitative tools for landslide risk classification and early-warning threshold determination. This study proposes a novel technical approach for high-precision slope stability evaluation and provides essential theoretical foundations and practical support for decision-making in geological hazard prevention and control. The study demonstrates significant engineering applicability and shows promise for broader implementation.